Question

1. Find the cube root of each of the following numbers by prime factorisation method.
m 512
m 10648
(iv) 27000
(v) 15625
(vi) 13824
(vi) 110592 (vi) 46656
x 175616 (x) 91125​

Answer 1

Answer:

512 = 8

10648 = 22

27000 = 30

15625 = 25

110592 = 48

46656 = 36

175616 = 56

91125 = 45

Step-by-step explanation:

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Answer 2

Solution:

prime factorization is given below

 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

          = 2³x 2³ x 2³

³√512 =   2×2×2=8

10648 = 2 x 2 x 2 x 11 x 11 x 11

             = 2³ x 11³

³√10648 =   2×11=22

 27000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5

                  = 2³ x 3³ x 5³

³√27000 =   2×3×5=30

15625 = 5 x 5 x 5 x 5 x 5 x 5

                 = 5³x 5³

∛15625 =   5×5=25

13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

               = 2³x 2³ x 2³ x 3³

³√13824 =   2×2×2×3=24

110592 = 2³ x 2³ x 2³ x 2³ x 3³

∛110592 =   2×2×2×2×3=48

46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

                = 2³ x 2³ x 3³x 3³

³√46656 =   2×2×3×3=36

175616 = 2³x 2³ x 2³ x 7³

³√175616 =   2×2×2×7=56

91125 = 5³ x 3³ x 3³

³√91125 =   5×3×3=45